Jonathan D. Wolfe

An Instrumentation System Applied to Formation Flight

As part of a NASA dryden autonomous formation flight program for improved drag reduction of multiple F/A-18 aircraft, a new instrument, the formation flight instrumentation system (FFIS), for the precise estimation of the relative position, velocity, and attitude between two moving aircraft without the aid of ground-based instruments, was developed. The FFIS uses a global position system (GPS) receiver and an inertial navigation sensor (INS) instrumentation package on each aircraft combined with a wireless communication system for sharing measurements between vehicles. An extended Kalman filter structure blends the outputs of each GPS/INS in a distributed manner so as to maximize the accuracy of the relative state estimates. Differential carrier phase GPS measurements are used to provide high accuracy relative range measurements to the filtering algorithm. A multiple hypothesis Wald test for estimating the integer ambiguity between the two moving vehicles was developed as part of this project. The FFIS was tested in a hardware-in-the-loop simulation (HIL Sim) before being tested in actual F-18 flight tests. Test results validated the FFIS performance. Flight test results showed that the Wald test accurately estimates the integer ambiguity and that relative range estimates using least squares provide accurate position estimates with a mean of approximately 7 cm and a standard deviation of 13 cm

Optimal planning for autonomous air vehicle battle management

We formulate a dynamic air vehicle assignment problem to sequentially determine the optimal allocation of air vehicle and ammunition resources to threat clusters in an air to ground campaign. A threat cluster includes a number of different types of threats, which are assumed to cooperate among themselves when they are engaged by a team of air vehicles. The objective is to efficiently allocate the assets to eliminate as many valuable threats as possible while minimizing the air vehicle attrition. This problem is formulated as an optimal control problem, whose exact solution can be obtained for small size problems by dynamic programming. For larger more realistic problems, we investigate hierarchical control and potential function methods to solve the optimal control problem in a computationally efficient manner.

Estimation of relative satellite position using transformed differential carrier-phase GPS measurements

Techniques for applying differential carrier-phase global positioning systems to satellite formation clusters with large (approximately 100 km or more) baselines are described. Because satellites in the cluster may move relative to each other, it is imperative that the carrier-phase ambiguities be resolved quickly and accurately. We propose a transformation of the m-vector carrier-phase measurement equations that restricts the geometric nonlinearities to a one-dimensional subspace and an almost universal linearization of the position state and integer ambiguities in the remaining m - 1 dimensional subspace. We then show that all of the measurement equations can be processed with an unscented Kalman filter to quickly compute very accurate floating-point valued estimates of the system state and error covariance. By an integer-preserving transformation found in the least-squares ambiguity decorrelation adjustment method, the number of possible hypotheses for the double-differenced wide-lane ambiguity candidates can be reduced. For the hypotheses set applying a multiple hypothesis Wald sequential probability test, using a specially conditioned form of the transformed global positioning system measurements, quickly and almost optimally determines the correct value of the carrier-phase double-differenced ambiguity. Once the double-differenced wide-lane ambiguities are obtained, the L 1 double-differenced ambiguities are resolved by using L 1 and L 2 carrier-phase measurements based on wide-lane integers in the unscented Kalman filter, then using the least-squares ambiguity decorrelation adjustment method for determining the hypotheses, followed by the multiple hypothesis Wald sequential probability test for resolving the L 1 double-differenced ambiguities. Finally, using the L 1 carrier-phase measurements, the unscented Kalman filter produces the relative position estimates. These techniques are then demonstrated on a simulation of a formation of two satellites in low Earth orbits.

Effective Estimation of Relative Positions in Orbit Using Differential Carrier-Phase GPS

Although dierential carrier phase GPS measurements are very accurate, their applications have heretofore been restricted to short baselines. In this paper we describe methods that allow very accurate estimation of the baseline vector over long distances in near-Earth space using dierential carrier phase GPS measurements. These estimates can enable many proposed satellite formation cluster projects.

A low-power filtering scheme for distributed sensor networks

Because the energy required for communications tasks is much greater than that required for computational tasks, estimation algorithms designed for distributed networks of sensors must attempt to reduce the communications overhead that they require. We suggest a simple mechanism for implementing Luenberger observers that allows estimates to be constructed from transmissions generated at a slower rate than the measurements are collected, while maintaining a robustness to communications outages, interruptions and delays.

A two-station decentralized LQG problem with noisy communication

We consider a two-station decentralized linear quadratic Gaussian problem, where the stations are allowed to communicate some pieces of information. We investigate a possible sub-optimal approach where the controls are obtained based on two separate centralized problems. Various cases are considered in which the two stations communicate their measurements, their controls or estimates, and their estimation residual through noisy channels. We mainly focus on the closed-loop stability properties. We show that even if the stations communicate all their measurements through low noise or even noiseless channels, the controls obtained from the two centralized LQG problems may fail to stabilize the closed-loop decentralized system.

Brief The periodic optimality of LQ controllers satisfying strong stabilization

An LQ strong stabilization problem is proposed. To determine when a controller with periodic gains is locally superior to a linear time invariant compensator for this problem, a @P test is presented. For systems with strictly proper transfer functions, it is proven that the frequency range where stable periodic controllers based on weak variations about the LTI case can give better performance than stable LTI compensators is finite. In the development, a means to evaluate the second partials of functions with respect to matrix-valued parameters is introduced. For those systems where periodic control is warranted, techniques for designing optimal periodic strongly stabilizing controllers are presented. Two examples detailing the application of the @P test are provided, as well as an optimal periodic controller design example.

Improved Integer Ambiguity Resolution Technique for Fixed Arrays

A method for quickly and accurately determining the integer ambiguities associated with carrier phase measurements on a rigid antenna array is presented. Residuals generated from the difference between the global positioning system measurements and the hypothesized value have been used in the multiple-hypothesis Wald sequential probability test (MHWSPT) to resolve the integer ambiguities. The new technique involves augmenting these residuals with new residuals constructed from the known baseline distances between the antennas in the array. Experimental results using this augmented set of residuals in the MHWSPT demonstrate an approximately eightfold reduction compared to that using only the residual set without augmentation in the time required to determine the integer ambiguities to desired levels of certainty.

The periodic optimality of LQ controllers satisfying strong stabilization

We present a /spl Pi/ test for determining when a controller with periodic gains is superior to a LTI compensator for a class of LQ strong stabilization problems. In our development, we also introduce means to evaluate the second partials of cost functions dependent on matrix valued parameters.

An efficient design algorithm for optimal fixed structure control

An extremely flexible design method for developing optimal fixed structure controllers is to place the cost of subsystem interconnections in the cost function. The optimal gain is then obtained via a numerical search procedure. Previous work with this class of cost functions has only made use of steepest-descent searches. In this paper, a descent function search algorithm is presented that significantly decreases the number of iterations needed to converge. An example shows that the descent function algorithm has superior convergence properties.